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Introduction
Quantum Mechanics
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Introduction
Intended audience
Major Sources
Aim of Course
Outline of Course
Probability Theory
Introduction
What is Probability?
Combining Probabilities
Mean, Variance, and Standard Deviation
Continuous Probability Distributions
Exercises
Wave-Particle Duality
Introduction
Wavefunctions
Plane Waves
Representation of Waves via Complex Functions
Classical Light Waves
Photoelectric Effect
Quantum Theory of Light
Classical Interference of Light Waves
Quantum Interference of Light
Classical Particles
Quantum Particles
Wave Packets
Evolution of Wave Packets
Heisenberg's Uncertainty Principle
Schrödinger's Equation
Collapse of the Wave Function
Exercises
Fundamentals of Quantum Mechanics
Introduction
Schrödinger's Equation
Normalization of the Wavefunction
Expectation Values and Variances
Ehrenfest's Theorem
Operators
Momentum Representation
Heisenberg's Uncertainty Principle
Eigenstates and Eigenvalues
Measurement
Continuous Eigenvalues
Stationary States
Exercises
One-Dimensional Potentials
Introduction
Infinite Potential Well
Square Potential Barrier
WKB Approximation
Cold Emission
Alpha Decay
Square Potential Well
Simple Harmonic Oscillator
Exercises
Multi-Particle Systems
Introduction
Fundamental Concepts
Non-Interacting Particles
Two-Particle Systems
Identical Particles
Exercises (N.B. Neglect spin in the following questions.)
Three-Dimensional Quantum Mechanics
Introduction
Fundamental Concepts
Particle in a Box
Degenerate Electron Gases
White-Dwarf Stars
Exercises
Orbital Angular Momentum
Introduction
Angular Momentum Operators
Representation of Angular Momentum
Eigenstates of Angular Momentum
Eigenvalues of
Eigenvalues of
Spherical Harmonics
Exercises
Central Potentials
Introduction
Derivation of Radial Equation
Infinite Spherical Potential Well
Hydrogen Atom
Rydberg Formula
Exercises
Spin Angular Momentum
Introduction
Spin Operators
Spin Space
Eigenstates of
and
Pauli Representation
Spin Precession
Exercises
Addition of Angular Momentum
Introduction
General Principles
Angular Momentum in the Hydrogen Atom
Two Spin One-Half Particles
Exercises
Time-Independent Perturbation Theory
Introduction
Improved Notation
Two-State System
Non-Degenerate Perturbation Theory
Quadratic Stark Effect
Degenerate Perturbation Theory
Linear Stark Effect
Fine Structure of Hydrogen
Zeeman Effect
Hyperfine Structure
Time-Dependent Perturbation Theory
Introduction
Preliminary Analysis
Two-State System
Spin Magnetic Resonance
Perturbation Expansion
Harmonic Perturbations
Electromagnetic Radiation
Electric Dipole Approximation
Spontaneous Emission
Radiation from a Harmonic Oscillator
Selection Rules
Transitions in Hydrogen
Intensity Rules
Forbidden Transitions
Variational Methods
Introduction
Variational Principle
Helium Atom
Hydrogen Molecule Ion
Scattering Theory
Introduction
Fundamentals
Born Approximation
Partial Waves
Determination of Phase-Shifts
Hard Sphere Scattering
Low Energy Scattering
Resonances
About this document ...
Richard Fitzpatrick 2010-07-20
Transitions in Hydrogen
and 